I spent most of the day grading extended problem solving papers. The school at which I teach is using a reform math curriculum. There are Problems of the Week (POW’s) which are problems (usually topics in discrete mathematics) which require the students to write an extended response including: rephrasing the problem in their own words, describing the process they used, stating and defending their solution, and evaluating the problem.

Most students did a nice job of systematically approaching the problem (looking for patterns and making generalizations). I was, however, surprised by the number of students that misread the problem. A few thought it said, “when placed into groups of 2, 3, 4, 5, or 6 there was at least one left over” – the problem said one left over. Needless to say, this changed the way they attacked the problem. Another issue was students putting additional constraints on the problem that weren’t there to begin with.

This was after we had read the problem as a class, had a discussion about the constraints, they completed a homework assignment explaining why the answer was not 49, and discussed the problem the next day.

So my questions are:

1) How do you handle reading in a mathematics classroom?

2) How do you deal with grading extended response problems? I’m thinking of the time commitment involved in providing meaningful feedback, even when using a rubric (insights from any English teachers out there would be appreciated).

Thanks, The person trying to figure out how to remain anonymous and yet still have a name.
Jackie

8 Responses to Mis-Reading in Mathematics

That sounds like good old IMP. I think I remember actually doing that problem a few years back. When we first developed our Algebra 1 course, we wanted to incorporate IMP POWs as a part of the curriculum. We found that it took nearly a semester for the freshmen to be able to just write a good problem statement, let alone actually learn problem solving heuristics and justify their answers.

If lots of students are misreading the problem, then maybe you can have them first turn in their problem statements. These can be evaluated by peers or by you, edited, and rewritten as needed.

A good thing to do is to make overheads of different students’ problem statements (names removed, of course) that show different levels of quality, or different problems/successes you want to point out. You can “grade” them on the overhead in front of the class so they can better understand your thought process.

You can also combine this overhead grading with the rubric process for giving feedback on the other parts of the POWs. This way, you can pick some model papers (F, C, B, A or whatever scale you have) and make specific comments that the whole class can hear at once, instead of writing the same thing again and again.

Another thing you can do with grading is decide to really focus in on one aspect for each POW. Maybe you read and respond to the problem statement carefully one time, and holistically grade the rest. Maybe the next time you do it for the justification.

One nice thing for reading in class is the “think aloud”. You put a piece of text on the overhead, and read it aloud to the class, also saying out loud your thought process. But you come up with a sign to indicate when you are thinking versus reading (i.e. hand on my head means I am thinking). That way, you can model how you actually read text in math, including questioning, restating, re-reading, etc. It will take a lot of repetition and practice, but if you do this often, it could help them understand what they need to focus on when reading in math.

I realize that it will be a process for the freshmen. I actually did do much of what you suggested. The homework the night the POW was assigned was to write the problem statement. The next day in class, we posted samples from each group around the room. Then we discussed the pros and cons of each. I think this helped most of the students.

It was just the few (5-10%) that totally misread it after this process that surprised me. Silly me to think everyone was paying attention in class! Actually, I’m quite happy with most of what was submitted. The presentations were pretty good too– as were the ensuing discussions (considering it was the third week of school).

I really like the idea of focusing on one aspect to grade each time. I think I may try that with the next one we assign. Thanks for the tips!

Jackie,
Misreading problems is often times seen with kids with reading disabilities and is a killer for them. People forget how much reading is actually involved with Math problems.
I don’t really have an answer other than to make sure your problems use clear language, (avoid the use of “not” for example) and encourage the students to first read through the entire problem as many time as they need to. Students with reading disabilities often times glance through the problem looking for key words but missing other key points. Their reading avoidance impacts their reading of math problems as well.

I agree that many students (not just those with diagnosed disabilities) glance or “skim and scan” through a problem. To try to get them in the habit of carefully reading the problems and determining the meaning is one of things on which I am working with the freshmen.

To do this, the students will read the problem aloud, then I’ll ask for someone to rephrase the problem in their own words. This usually takes awhile before we can agree that the summary matches the text and often leads us to re-reading the problem.

Do we get through fewer problems this way? Yep – but I’d rather have them develop the habit/skill of carefully reading and understanding the problems we do get through.

My hope is that this practice will become part of their “toolkit” that they can use when working on problems at home and in the future.

Some time soon, I’ll update the “About” page to include a bit more about my past experiences (although I’m a first year teacher, I have ten years of experience as a special education assistant).

IMP! Dan beat me to it. You know, I just collected some problem write-ups. And just now I skimmed them. A few were nice. Mostly mediocre (reasonable conclusions with incomplete supporting work) and a few weak ones. I will grade them for completeness (1 or 0), and discuss what made some good, and maybe pass out samples.

And we’ll do it again.

Now, they worked in class, in groups of 3. And while I didn’t watch solutions come from each table, I did stop long enough to make sure that we had a shared understanding. And then what they did together they did together, what they did at home they did at home, but the understanding was shared.